The phase-field-crystal model is by now widely used in order to predict crystal nucleation and growth. For colloidal solidification with completely overdamped individual particle motion, we show that the phase-field-crystal dynamics can be derived from the microscopic Smoluchowski equation via dynamical density-functional theory. The different underlying approximations are discussed. In particular, a variant of the phase-field-crystal model is proposed which involves less approximations than the standard phase-field-crystal model. We finally test the validity of these phase-field-crystal models against dynamical density-functional theory. In particular, the velocities of a linear crystal front from the undercooled melt are compared as a function of the undercooling for a two-dimensional colloidal suspension of parallel dipoles. Good agreement is only obtained by a drastic scaling of the free energies in the phase-field-crystal model in order to match the bulk freezing transition point.

Si-based nanoarchitectures are formed with unprecedented precision and reproducibility via templated dewetting of thin SOI.

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One of the major difficulties in employing phase field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the new term is explored in 2D triangular and honeycomb structures as well as bcc and fcc lattices in 3D. In addition, a Finite Element Method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.

Several crystalline structures of present interest are metastable or kinetically-frozen out-of-equilibrium states in the phase space. When the corresponding lifetime is sufficently long, typical equilibrium features such as regular, extended faceting can be observed. However, interpreting the extension of the facets and the overall shape in terms of a simple Wulff analysis is not justified. Here we introduce a convenient general formulation of the anisotropic surface energy density which, combined with a suitable Phase-Field model of surface diffusion, allows for the investigation of the evolution toward equilibrium of three-dimensional nanostructures characterized by arbitrary facets.

We address a three-dimensional, coarse-grained description of dislocation networks at grain boundaries between rotated crystals. The so-called amplitude expansion of the phase-field crystal model is exploited with the aid of finite element method calculations. This approach allows for the description of microscopic features, such as dislocations, while simultaneously being able to describe length scales that are orders of magnitude larger than the lattice spacing. Moreover, it allows for the direct description of extended defects by means of a scalar order parameter. The versatility of this framework is shown by considering both fcc and bcc lattice symmetries and different rotation axes. First, the specific case of planar, twist grain boundaries is illustrated. The details of the method are reported and the consistency of the results with literature is discussed. Then, the dislocation networks forming at the interface between a spherical, rotated crystal embedded in an unrotated crystalline structure, are shown. Although explicitly accounting for dislocations which lead to an anisotropic shrinkage of the rotated grain, the extension of the spherical grain boundary is found to decrease linearly over time in agreement with the classical theory of grain growth and recent atomistic investigations. It is shown that the results obtained for a system with bcc symmetry agree very well with existing results, validating the methodology. Furthermore, fully original results are shown for fcc lattice symmetry, revealing the generality of the reported observations. arXiv:1803.03233v2 [cond-mat.mtrl-sci]

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If two-dimensional crystals grow on a curved surface, the Gaussian curvature of the surface induces elastic stress and affects the growth pathway. The elastic stress can be alleviated by incorporating defects or, if this is energetically unfavorable, via an elastic instability which leads to anisotropic growth with branched ribbonlike structures. This instability provides a generic route to grow defect-free crystals on curved surfaces. Depending on the elastic properties of the crystal and the geometric properties of the surface, different growth morphologies with two-, four-, and sixfold symmetry develop. Using a phase field crystal type modeling approach, we provide a microscopic understanding of the morphology selection.